AP Physics C: Mechanics, AP exams

Unit 2: Force and Translational Dynamics

Unit 2 develops Newton's laws with calculus-capable force models. Resistive forces that depend on velocity, such as air drag, are the signature addition, along with terminal velocity as the solution of a differential equation. Gravitation appears here as a force law rather than as a separate unit.

Position: 2 of 7 units
Topics covered: 6 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics C: Mechanics. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Systems, forces, and free-body diagrams: Choosing a system, identifying all interactions, and translating a diagram into equations of motion.
Newton's laws applied: Connected bodies, inclines, pulleys, and force pairs analyzed with consistent coordinate choices.
Friction and spring forces: Static and kinetic friction, and the linear restoring force of an ideal spring.
Resistive forces and terminal velocity: Velocity-dependent drag, the resulting differential equation, and the approach to terminal speed.
Gravitation: The universal law of gravitation, gravitational field, and the force inside and outside a spherical body.
Circular motion: Centripetal acceleration, the net inward force requirement, and applications including orbital motion.

Study tips

How to practice Force and Dynamics.

Section-specific guidance that follows from how this material is usually tested.

Set up the drag differential equation from a free-body diagram at least a few times; recognizing the setup is most of the work.
Sketch the velocity-versus-time curve approaching terminal velocity and be able to explain its shape.
Choose coordinate axes along the acceleration direction on inclines; it removes most of the algebra.

Where this fits

Unit 2: Force and Translational Dynamics is 2 of 7 units in the AP Physics C: Mechanics guide. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics C: Mechanics guide Official exam information

Sample Force and Dynamics questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
True or false: for a book lying at rest on a horizontal table, the upward normal force from the table is the Newton's third law reaction to the book's weight.
1. ATrue
2. BFalse
Show answer
Answer: B. False
A third law pair acts on two different objects and involves the same type of interaction, so the partner of Earth's gravitational pull on the book is the book's gravitational pull on Earth. The normal force and the weight happen to be equal here only because the book has zero acceleration, and they act on the same object.
Key insight: Third law partners never appear on the same free-body diagram, because they act on different objects.
Question 2Foundational
The gravitational field strength at the surface of a spherical planet of radius R is 12 N/kg. What is the gravitational field strength at a point 2R from the planet's center?
1. A1.5 N/kg
2. B3.0 N/kg
3. C6.0 N/kg
4. D24 N/kg
Show answer
Answer: B. 3.0 N/kg
Outside a spherical body the field falls off as 1/r^2, so doubling the distance from the center divides the field by 4: 12/4 = 3.0 N/kg. The 6.0 N/kg choice halves the field, treating it as inversely proportional to distance.
Key insight: Gravitational distances are measured from the center of the body, not from its surface.
Question 3Intermediate
A block slides down an incline that makes an angle of 37 degrees with the horizontal, where sin(37 degrees) = 0.60 and cos(37 degrees) = 0.80. The coefficient of kinetic friction between block and incline is 0.20 and g = 10 m/s^2. What is the magnitude of the block's acceleration?
1. A2.0 m/s^2
2. B4.4 m/s^2
3. C6.0 m/s^2
4. D7.6 m/s^2
Show answer
Answer: B. 4.4 m/s^2
Along the incline, a = g[sin(theta) - (mu)cos(theta)] = 10[0.60 - (0.20)(0.80)] = 10(0.44) = 4.4 m/s^2, and the mass cancels. The 6.0 m/s^2 choice is the frictionless result, and 7.6 m/s^2 adds the friction term instead of subtracting it.
Key insight: Choosing axes along and perpendicular to the incline keeps the acceleration on a single axis.
Question 4Intermediate
A 2.0 kg object falls through a fluid that exerts a resistive force of magnitude bv opposing the motion, with b = 5.0 kg/s. Using g = 10 m/s^2, what is the terminal speed of the object?
1. A2.5 m/s
2. B4.0 m/s
3. C10 m/s
4. D100 m/s
Show answer
Answer: B. 4.0 m/s
Terminal speed occurs when the acceleration is zero, so mg = bv and v = mg/b = (2.0)(10)/5.0 = 4.0 m/s. The 2.5 m/s choice divides b by the mass rather than dividing the weight by b.
Key insight: Terminal velocity is a force balance, so it is found by setting the acceleration to zero rather than by solving the full differential equation.
Question 5Advanced
An object released from rest falls under gravity while a resistive force proportional to its speed acts on it. Using g = 10 m/s^2, what is the magnitude of its acceleration at the instant its speed equals half the terminal speed?
1. A0 m/s^2
2. B2.5 m/s^2
3. C5.0 m/s^2
4. D10 m/s^2
Show answer
Answer: C. 5.0 m/s^2
Newton's second law gives ma = mg - bv, and since bv_terminal = mg, at v = v_terminal/2 the drag is mg/2 and the net force is mg/2, so a = g/2 = 5.0 m/s^2. The 10 m/s^2 choice ignores the drag force that has already built up.
Key insight: In linear-drag free fall the acceleration falls off in proportion to how much of the terminal speed has been reached.

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Unit 2: Force and Translational Dynamics